"""

Copyright 2013 Steven Diamond, 2017 Robin Verschueren

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
"""
import unittest

import numpy as np
import scipy.sparse as sp
from scipy.linalg import lstsq

import cvxpy as cp
import cvxpy.tests.solver_test_helpers as sths
from cvxpy import Maximize, Minimize, Parameter, Problem
from cvxpy.atoms import (
    QuadForm,
    abs,
    huber,
    matrix_frac,
    norm,
    power,
    quad_over_lin,
    sum,
    sum_squares,
)
from cvxpy.expressions.variable import Variable
from cvxpy.reductions.solvers.defines import (
    INSTALLED_CONIC_SOLVERS,
    INSTALLED_SOLVERS,
    QP_SOLVERS,
    SOLVER_MAP_CONIC,
)
from cvxpy.tests.base_test import BaseTest
from cvxpy.tests.solver_test_helpers import SolverTestHelper, StandardTestLPs, StandardTestQPs


class QPTestBase(BaseTest):
    """Base class with shared test helpers for QP-style problems."""

    def setUp(self) -> None:
        self.a = Variable(name='a')
        self.b = Variable(name='b')
        self.c = Variable(name='c')

        self.x = Variable(2, name='x')
        self.y = Variable(3, name='y')
        self.z = Variable(2, name='z')
        self.w = Variable(5, name='w')

        self.A = Variable((2, 2), name='A')
        self.B = Variable((2, 2), name='B')
        self.C = Variable((3, 2), name='C')

        self.slope = Variable(1, name='slope')
        self.offset = Variable(1, name='offset')
        self.quadratic_coeff = Variable(1, name='quadratic_coeff')

        T = 30
        self.position = Variable((2, T), name='position')
        self.velocity = Variable((2, T), name='velocity')
        self.force = Variable((2, T - 1), name='force')

        self.xs = Variable(80, name='xs')
        self.xsr = Variable(50, name='xsr')
        self.xef = Variable(80, name='xef')

    def solve_QP(self, problem, solver_name):
        """Override in subclasses."""
        raise NotImplementedError

    # License checking helpers - shared by subclasses
    @staticmethod
    def is_mosek_available():
        """Check if MOSEK is installed and a license is available."""
        if 'MOSEK' not in INSTALLED_SOLVERS:
            return False
        try:
            import mosek  # type: ignore
            env = mosek.Env()
            status = env.getlicense()
            return status == mosek.rescode.ok
        except Exception:
            return False

    @staticmethod
    def is_knitro_available():
        """Check if KNITRO is installed and a license is available."""
        if 'KNITRO' not in INSTALLED_SOLVERS:
            return False
        try:
            import knitro  # type: ignore
            kc = knitro.KN_new()
            if kc is None:
                return False
            knitro.KN_free(kc)
            return True
        except Exception:
            return False

    @staticmethod
    def is_xpress_available():
        """Check if XPRESS is installed and a license is available."""
        if 'XPRESS' not in INSTALLED_SOLVERS:
            return False
        try:
            import xpress  # type: ignore
            env = xpress.env()
            status = env.getlicense()
            return status == 0
        except Exception:
            return False

    def filter_licensed_solvers(self, solvers):
        """Remove solvers that don't have valid licenses."""
        result = list(solvers)
        if 'XPRESS' in result and not self.is_xpress_available():
            result.remove('XPRESS')
        if 'MOSEK' in result and not self.is_mosek_available():
            result.remove('MOSEK')
        if 'KNITRO' in result and not self.is_knitro_available():
            result.remove('KNITRO')
        return result

    def _check_kkt(self, problem, places=4):
        """Verify KKT conditions for a solved problem."""
        obj_pair = (problem.objective, None)
        var_pairs = [(v, None) for v in problem.variables()]
        con_pairs = [(c, None) for c in problem.constraints]
        sth = SolverTestHelper(obj_pair, var_pairs, con_pairs)
        # Problem already solved, just use the same problem object
        sth.prob = problem
        sth.check_primal_feasibility(places)
        sth.check_complementarity(places)
        sth.check_dual_domains(places)
        sth.check_stationary_lagrangian(places)

    # Test helper methods - shared by all subclasses
    def quad_over_lin(self, solver) -> None:
        p = Problem(Minimize(0.5 * quad_over_lin(abs(self.x-1), 1)),
                    [self.x <= -1])
        self.solve_QP(p, solver)
        for var in p.variables():
            self.assertItemsAlmostEqual(np.array([-1., -1.]),
                                        var.value, places=4)
        for con in p.constraints:
            self.assertItemsAlmostEqual(np.array([2., 2.]),
                                        con.dual_value, places=4)
        self._check_kkt(p, places=3)

    def abs(self, solver) -> None:
        u = Variable(2)
        constr = []
        constr += [abs(u[1] - u[0]) <= 100]
        prob = Problem(Minimize(sum_squares(u)), constr)
        print("The problem is QP: ", prob.is_qp())
        self.assertEqual(prob.is_qp(), True)
        result = prob.solve(solver=solver)
        self.assertAlmostEqual(result, 0)

    def power(self, solver) -> None:
        p = Problem(Minimize(sum(power(self.x, 2))), [])
        self.solve_QP(p, solver)
        for var in p.variables():
            self.assertItemsAlmostEqual([0., 0.], var.value, places=4)

    def power_matrix(self, solver) -> None:
        p = Problem(Minimize(sum(power(self.A - 3., 2))), [])
        self.solve_QP(p, solver)
        for var in p.variables():
            self.assertItemsAlmostEqual([3., 3., 3., 3.],
                                        var.value, places=4)

    def square_affine(self, solver) -> None:
        A = np.random.randn(10, 2)
        b = np.random.randn(10)
        p = Problem(Minimize(sum_squares(A @ self.x - b)))
        self.solve_QP(p, solver)
        for var in p.variables():
            self.assertItemsAlmostEqual(lstsq(A, b)[0].flatten(order='F'), var.value,
                                        places=1)

    def quad_form(self, solver) -> None:
        np.random.seed(0)
        A = np.random.randn(5, 5)
        z = np.random.randn(5)
        P = A.T.dot(A)
        q = -2*P.dot(z)
        p = Problem(Minimize(QuadForm(self.w, P) + q.T @ self.w))
        self.solve_QP(p, solver)
        for var in p.variables():
            self.assertItemsAlmostEqual(z, var.value, places=4)

    def rep_quad_form(self, solver) -> None:
        """A problem where the quad_form term is used multiple times.
        """
        np.random.seed(0)
        A = np.random.randn(5, 5)
        z = np.random.randn(5)
        P = A.T.dot(A)
        q = -2*P.dot(z)
        qf = QuadForm(self.w, P)
        p = Problem(Minimize(0.5*qf + 0.5*qf + q.T @ self.w))
        self.solve_QP(p, solver)
        for var in p.variables():
            self.assertItemsAlmostEqual(z, var.value, places=4)

    def affine_problem(self, solver) -> None:
        np.random.seed(0)
        A = np.random.randn(5, 2)
        A = np.maximum(A, 0)
        b = np.random.randn(5)
        b = np.maximum(b, 0)
        p = Problem(Minimize(sum(self.x)), [self.x >= 0, A @ self.x <= b])
        self.solve_QP(p, solver)
        for var in p.variables():
            self.assertItemsAlmostEqual([0., 0.], var.value, places=3)
        self._check_kkt(p, places=3)

    def maximize_problem(self, solver) -> None:
        np.random.seed(0)
        A = np.random.randn(5, 2)
        A = np.maximum(A, 0)
        b = np.random.randn(5)
        b = np.maximum(b, 0)
        p = Problem(Maximize(-sum(self.x)), [self.x >= 0, A @ self.x <= b])
        self.solve_QP(p, solver)
        for var in p.variables():
            self.assertItemsAlmostEqual([0., 0.], var.value, places=3)
        self._check_kkt(p, places=3)

    def norm_2(self, solver) -> None:
        A = np.random.randn(10, 5)
        b = np.random.randn(10)
        p = Problem(Minimize(norm(A @ self.w - b, 2)))
        self.solve_QP(p, solver)
        for var in p.variables():
            self.assertItemsAlmostEqual(lstsq(A, b)[0].flatten(order='F'), var.value,
                                        places=1)

    def mat_norm_2(self, solver) -> None:
        A = np.random.randn(5, 3)
        B = np.random.randn(5, 2)
        p = Problem(Minimize(norm(A @ self.C - B, 2)))
        s = self.solve_QP(p, solver)
        for var in p.variables():
            self.assertItemsAlmostEqual(lstsq(A, B)[0],
                                        s.primal_vars[var.id], places=1)

    def quad_form_coeff(self, solver) -> None:
        np.random.seed(0)
        A = np.random.randn(5, 5)
        z = np.random.randn(5)
        P = A.T.dot(A)
        q = -2*P.dot(z)
        p = Problem(Minimize(QuadForm(self.w, P) + q.T @ self.w))
        self.solve_QP(p, solver)
        for var in p.variables():
            self.assertItemsAlmostEqual(z, var.value, places=4)

    def quad_form_bound(self, solver) -> None:
        P = np.array([[13, 12, -2], [12, 17, 6], [-2, 6, 12]])
        q = np.array([[-22], [-14.5], [13]])
        r = 1
        y_star = np.array([[1], [0.5], [-1]])
        p = Problem(Minimize(0.5*QuadForm(self.y, P) + q.T @ self.y + r),
                    [self.y >= -1, self.y <= 1])
        self.solve_QP(p, solver)
        for var in p.variables():
            self.assertItemsAlmostEqual(y_star, var.value, places=4)
        self._check_kkt(p)

    def regression_1(self, solver) -> None:
        np.random.seed(1)
        # Number of examples to use
        n = 100
        # Specify the true value of the variable
        true_coeffs = np.array([[2, -2, 0.5]]).T
        # Generate data
        x_data = np.random.rand(n) * 5
        x_data = np.atleast_2d(x_data)
        x_data_expanded = np.vstack([np.power(x_data, i)
                                     for i in range(1, 4)])
        x_data_expanded = np.atleast_2d(x_data_expanded)
        y_data = x_data_expanded.T.dot(true_coeffs) + 0.5 * np.random.rand(n, 1)
        y_data = np.atleast_2d(y_data)

        line = self.offset + x_data * self.slope
        residuals = line.T - y_data
        fit_error = sum_squares(residuals)
        p = Problem(Minimize(fit_error), [])
        self.solve_QP(p, solver)
        self.assertAlmostEqual(1171.60037715, p.value, places=4)

    def regression_2(self, solver) -> None:
        np.random.seed(1)
        # Number of examples to use
        n = 100
        # Specify the true value of the variable
        true_coeffs = np.array([2, -2, 0.5])
        # Generate data
        x_data = np.random.rand(n) * 5
        x_data_expanded = np.vstack([np.power(x_data, i)
                                     for i in range(1, 4)])
        print(x_data_expanded.shape, true_coeffs.shape)
        y_data = x_data_expanded.T.dot(true_coeffs) + 0.5 * np.random.rand(n)

        quadratic = self.offset + x_data * self.slope + \
            self.quadratic_coeff*np.power(x_data, 2)
        residuals = quadratic.T - y_data
        fit_error = sum_squares(residuals)
        p = Problem(Minimize(fit_error), [])
        self.solve_QP(p, solver)

        self.assertAlmostEqual(139.225660756, p.value, places=4)

    def control(self, solver) -> None:
        # Some constraints on our motion
        # The object should start from the origin, and end at rest
        initial_velocity = np.array([-20, 100])
        final_position = np.array([100, 100])
        T = 30  # The number of timesteps
        h = 0.1  # The time between time intervals
        mass = 1  # Mass of object
        drag = 0.1  # Drag on object
        g = np.array([0, -9.8])  # Gravity on object
        # Create a problem instance
        constraints = []
        # Add constraints on our variables
        for i in range(T - 1):
            constraints += [self.position[:, i + 1] == self.position[:, i] +
                            h * self.velocity[:, i]]
            acceleration = self.force[:, i]/mass + g - \
                drag * self.velocity[:, i]
            constraints += [self.velocity[:, i + 1] == self.velocity[:, i] +
                            h * acceleration]

        # Add position constraints
        constraints += [self.position[:, 0] == 0]
        constraints += [self.position[:, -1] == final_position]
        # Add velocity constraints
        constraints += [self.velocity[:, 0] == initial_velocity]
        constraints += [self.velocity[:, -1] == 0]
        # Solve the problem
        p = Problem(Minimize(.01 * sum_squares(self.force)), constraints)
        self.solve_QP(p, solver)
        self.assertAlmostEqual(1059.616, p.value, places=1)
        # KKT check skipped: check_stationary_lagrangian fails for 2D matrix
        # variables due to inconsistent gradient ordering (sum_squares uses
        # C order, constraint terms use F order). TODO fix this
        # self._check_kkt(p, places=3)

    def sparse_system(self, solver) -> None:
        m = 100
        n = 80
        np.random.seed(1)
        density = 0.4
        A = sp.random_array((m, n), density=density)
        b = np.random.randn(m)

        p = Problem(Minimize(sum_squares(A @ self.xs - b)), [self.xs == 0])
        self.solve_QP(p, solver)
        self.assertAlmostEqual(b.T.dot(b), p.value, places=4)

    def smooth_ridge(self, solver) -> None:
        np.random.seed(1)
        n = 50
        k = 20
        eta = 1

        A = np.ones((k, n))
        b = np.ones((k))
        obj = sum_squares(A @ self.xsr - b) + \
            eta*sum_squares(self.xsr[:-1]-self.xsr[1:])
        p = Problem(Minimize(obj), [])
        self.solve_QP(p, solver)
        self.assertAlmostEqual(0, p.value, places=4)

    def huber_small(self, solver, places=4) -> None:
        # Solve the Huber regression problem
        x = Variable(3)
        objective = sum(huber(x))

        # Solve problem with QP
        p = Problem(Minimize(objective), [x[2] >= 3])
        self.solve_QP(p, solver)
        self.assertAlmostEqual(3, x.value[2], places=places)
        self.assertAlmostEqual(5, objective.value, places=places)
        self._check_kkt(p, places=places)

    def huber(self, solver) -> None:
        # Generate problem data
        n = 3
        m = 5
        data = [0.89, 0.39, 0.96, 0.34, 0.68, 0.18, 0.63, 0.42, 0.51, 0.66, 0.43, 0.77]
        indices = [0, 1, 2, 3, 4, 2, 3, 0, 1, 2, 3, 4]
        indptr = [0, 5, 7, 12]
        A = sp.csc_array((data, indices, indptr), shape=(m, n))
        x_true = np.random.randn(n) / np.sqrt(n)
        ind95 = (np.random.rand(m) < 0.95).astype(float)
        b = A.dot(x_true) + np.multiply(0.5*np.random.randn(m), ind95) \
            + np.multiply(10.*np.random.rand(m), 1. - ind95)

        # Solve the Huber regression problem
        x = Variable(n)
        objective = sum(huber(A @ x - b))

        # Solve problem with QP
        p = Problem(Minimize(objective))
        self.solve_QP(p, solver)
        self.assertAlmostEqual(1.452797819667, objective.value, places=3)
        self.assertItemsAlmostEqual(x.value,
                                    [1.20524645, -0.85271489, -0.50838494],
                                    places=3)

    def equivalent_forms_1(self, solver) -> None:
        m = 100
        n = 80
        r = 70
        np.random.seed(1)
        A = np.random.randn(m, n)
        b = np.random.randn(m)
        G = np.random.randn(r, n)
        h = np.random.randn(r)

        obj1 = .1 * sum((A @ self.xef - b) ** 2)
        cons = [G @ self.xef == h]

        p1 = Problem(Minimize(obj1), cons)
        self.solve_QP(p1, solver)
        self.assertAlmostEqual(p1.value, 68.1119420108, places=4)
        self._check_kkt(p1, places=4)

    def equivalent_forms_2(self, solver) -> None:
        m = 100
        n = 80
        r = 70
        np.random.seed(1)
        A = np.random.randn(m, n)
        b = np.random.randn(m)
        G = np.random.randn(r, n)
        h = np.random.randn(r)

        # ||Ax-b||^2 = x^T (A^T A) x - 2(A^T b)^T x + ||b||^2
        P = np.dot(A.T, A)
        q = -2*np.dot(A.T, b)
        r = np.dot(b.T, b)

        obj2 = .1*(QuadForm(self.xef, P)+q.T @ self.xef+r)
        cons = [G @ self.xef == h]

        p2 = Problem(Minimize(obj2), cons)
        self.solve_QP(p2, solver)
        self.assertAlmostEqual(p2.value, 68.1119420108, places=4)
        self._check_kkt(p2, places=4)

    def equivalent_forms_3(self, solver) -> None:
        m = 100
        n = 80
        r = 70
        np.random.seed(1)
        A = np.random.randn(m, n)
        b = np.random.randn(m)
        G = np.random.randn(r, n)
        h = np.random.randn(r)

        # ||Ax-b||^2 = x^T (A^T A) x - 2(A^T b)^T x + ||b||^2
        P = np.dot(A.T, A)
        q = -2*np.dot(A.T, b)
        r = np.dot(b.T, b)
        Pinv = np.linalg.inv(P)

        obj3 = .1 * (matrix_frac(self.xef, Pinv)+q.T @ self.xef+r)
        cons = [G @ self.xef == h]

        p3 = Problem(Minimize(obj3), cons)
        self.solve_QP(p3, solver)
        print(solver)
        self.assertAlmostEqual(p3.value, 68.1119420108, places=4)
        self._check_kkt(p3, places=4)


class TestQp(QPTestBase):
    """Test native QP solvers."""

    def setUp(self) -> None:
        super().setUp()

        # Check for all installed QP solvers
        self.solvers = [x for x in QP_SOLVERS if x in INSTALLED_SOLVERS]
        self.solvers = self.filter_licensed_solvers(self.solvers)

    def solve_QP(self, problem, solver_name):
        return problem.solve(solver=solver_name, verbose=False)

    def test_all_solvers(self) -> None:
        for solver in self.solvers:
            self.quad_over_lin(solver)
            self.power(solver)
            self.power_matrix(solver)
            self.square_affine(solver)
            self.quad_form(solver)
            self.affine_problem(solver)
            self.maximize_problem(solver)
            self.abs(solver)

            # Do we need the following functionality?
            # self.norm_2(solver)
            # self.mat_norm_2(solver)

            self.quad_form_coeff(solver)
            self.quad_form_bound(solver)
            self.regression_1(solver)
            self.regression_2(solver)
            self.rep_quad_form(solver)

            # slow tests:
            self.control(solver)
            self.sparse_system(solver)
            self.smooth_ridge(solver)
            self.huber_small(solver)
            self.huber(solver)
            self.equivalent_forms_1(solver)
            self.equivalent_forms_2(solver)
            if solver != cp.KNITRO:
                self.equivalent_forms_3(solver)

    def test_warm_start(self) -> None:
        """Test warm start.
        """
        m = 200
        n = 100
        np.random.seed(1)
        A = np.random.randn(m, n)
        b = Parameter(m)

        # Construct the problem.
        x = Variable(n)
        prob = Problem(Minimize(sum_squares(A @ x - b)))

        b.value = np.random.randn(m)
        result = prob.solve(solver="OSQP", warm_start=False)
        result2 = prob.solve(solver="OSQP", warm_start=True)
        self.assertAlmostEqual(result, result2)
        b.value = np.random.randn(m)
        result = prob.solve(solver="OSQP", warm_start=True)
        result2 = prob.solve(solver="OSQP", warm_start=False)
        self.assertAlmostEqual(result, result2)

    def test_qpalm_warmstart(self) -> None:
        """Test warm start.
        """
        if cp.QPALM in INSTALLED_SOLVERS:
            m = 200
            n = 100
            np.random.seed(1)
            A = np.random.randn(m, n)
            b = Parameter(m)

            # Construct the problem.
            x = Variable(n)
            prob = Problem(Minimize(sum_squares(A @ x - b)))

            b.value = np.random.randn(m)
            result = prob.solve(solver=cp.QPALM, warm_start=False)
            result2 = prob.solve(solver=cp.QPALM, warm_start=True)
            self.assertAlmostEqual(result, result2)
            b.value = np.random.randn(m)
            result = prob.solve(solver=cp.QPALM, warm_start=True)
            result2 = prob.solve(solver=cp.QPALM, warm_start=False)
            self.assertAlmostEqual(result, result2)

    def test_gurobi_warmstart(self) -> None:
        """Test Gurobi warm start with a user provided point.
        """
        if cp.GUROBI in INSTALLED_SOLVERS:
            import gurobipy
            m = 4
            n = 3

            y = Variable(nonneg=True)
            X = Variable((m, n))
            X_vals = np.reshape(np.arange(m*n), (m, n))
            prob = Problem(Minimize(y**2 + cp.sum(X)), [X == X_vals])
            X.value = X_vals + 1
            prob.solve(solver=cp.GUROBI, warm_start=True)
            # Check that "start" value was set appropriately.
            model = prob.solver_stats.extra_stats
            model_x = model.getVars()
            assert gurobipy.GRB.UNDEFINED == model_x[0].start
            assert np.isclose(0, model_x[0].x)
            for i in range(1, X.size + 1):
                row = (i - 1) % X.shape[0]
                col = (i - 1) // X.shape[0]
                assert X_vals[row, col] + 1 == model_x[i].start
                assert np.isclose(X.value[row, col], model_x[i].x)

    def test_xpress_warmstart(self) -> None:
        """Test XPRESS warm start with a user provided point.
        """
        if cp.XPRESS in INSTALLED_SOLVERS:
            m = 20
            n = 10
            np.random.seed(1)
            A = np.random.randn(m, n)
            b = Parameter(m)

            # Construct the problem.
            x = Variable(n, integer=True)
            prob = Problem(Minimize(sum_squares(A @ x - b)))

            b.value = np.random.randn(m)
            result = prob.solve(solver=cp.XPRESS, warm_start=False)
            result2 = prob.solve(solver=cp.XPRESS, warm_start=True)
            self.assertAlmostEqual(result, result2)
            x.value = x.value.astype(np.int64)

            xprime = Variable(n, integer=True)
            prob = Problem(Minimize(sum_squares(A @ xprime - b)))
            xprime.value = x.value
            result = prob.solve(solver=cp.XPRESS, warm_start=True)
            result2 = prob.solve(solver=cp.XPRESS, warm_start=False)
            self.assertAlmostEqual(result, result2)

    def test_highs_warmstart(self) -> None:
        """Test warm start.
        """
        if cp.HIGHS in INSTALLED_SOLVERS:
            m = 200
            n = 100
            np.random.seed(1)
            A = np.random.randn(m, n)
            b = Parameter(m)

            # Construct the problem.
            x = Variable(n)
            prob = Problem(Minimize(sum_squares(A @ x - b)))

            b.value = np.random.randn(m)
            result = prob.solve(solver=cp.HIGHS, warm_start=False)
            result2 = prob.solve(solver=cp.HIGHS, warm_start=True)
            self.assertAlmostEqual(result, result2)
            b.value = np.random.randn(m)
            result = prob.solve(solver=cp.HIGHS, warm_start=True)
            result2 = prob.solve(solver=cp.HIGHS, warm_start=False)
            self.assertAlmostEqual(result, result2)

    def test_highs_cvar(self) -> None:
        """Test problem with CVaR constraint from
        https://github.com/cvxpy/cvxpy/issues/2836
        """
        if cp.HIGHS in INSTALLED_SOLVERS:
            # Generate data
            num_stocks = 5
            num_samples = 25
            np.random.seed(1)
            pnl_samples = np.random.uniform(low=0.0, high=1.0, size=(num_samples, num_stocks))
            pnl_expected = pnl_samples.mean(axis=0)

            # Prepare to solve
            quantile = 0.05
            w = cp.Variable(num_stocks, nonneg=True)
            cvar = cp.cvar(pnl_samples @ w, 1 - quantile)
            pnl = w @ pnl_expected

            # Solve
            objective = cp.Maximize(pnl)
            constraints = [cvar <= 0.5]
            problem = cp.Problem(objective, constraints)
            problem.solve(
                solver=cp.HIGHS,
            )
            assert problem.status == cp.OPTIMAL

    def test_piqp_warmstart(self) -> None:
        """Test warm start.
        """
        if cp.PIQP in INSTALLED_SOLVERS:
            m = 200
            n = 100
            np.random.seed(1)
            A = np.random.randn(m, n)
            b = Parameter(m)

            # Construct the problem.
            x = Variable(n)
            prob = Problem(Minimize(sum_squares(A @ x - b)))

            b.value = np.random.randn(m)
            result = prob.solve(solver=cp.PIQP, warm_start=False)
            result2 = prob.solve(solver=cp.PIQP, warm_start=True)
            self.assertAlmostEqual(result, result2)
            b.value = np.random.randn(m)
            result = prob.solve(solver=cp.PIQP, warm_start=True)
            result2 = prob.solve(solver=cp.PIQP, warm_start=False)
            self.assertAlmostEqual(result, result2)

    def test_parametric(self) -> None:
        """Test solve parametric problem vs full problem"""
        x = Variable()
        a = 10
        #  b_vec = [-10, -2., 2., 3., 10.]
        b_vec = [-10, -2.]

        for solver in self.solvers:

            print(solver)
            # Solve from scratch with no parameters
            x_full = []
            obj_full = []
            for b in b_vec:
                obj = Minimize(a * (x ** 2) + b * x)
                constraints = [0 <= x, x <= 1]
                prob = Problem(obj, constraints)
                prob.solve(solver=solver)
                x_full += [x.value]
                obj_full += [prob.value]

            # Solve parametric
            x_param = []
            obj_param = []
            b = Parameter()
            obj = Minimize(a * (x ** 2) + b * x)
            constraints = [0 <= x, x <= 1]
            prob = Problem(obj, constraints)
            for b_value in b_vec:
                b.value = b_value
                prob.solve(solver=solver)
                x_param += [x.value]
                obj_param += [prob.value]

            print(x_full)
            print(x_param)
            for i in range(len(b_vec)):
                self.assertItemsAlmostEqual(x_full[i], x_param[i], places=3)
                self.assertAlmostEqual(obj_full[i], obj_param[i])

    def test_square_param(self) -> None:
        """Test issue arising with square plus parameter.
        """
        a = Parameter(value=1)
        b = Variable()

        obj = Minimize(b ** 2 + abs(a))
        prob = Problem(obj)
        prob.solve(solver="SCS")
        self.assertAlmostEqual(obj.value, 1.0)

    def test_gurobi_time_limit_no_solution(self) -> None:
        """Make sure that if Gurobi terminates due to a time limit before finding a solution:
            1) no error is raised,
            2) solver stats are returned.
            The test is skipped if something changes on Gurobi's side so that:
            - a solution is found despite a time limit of zero,
            - a different termination criteria is hit first.
        """
        from cvxpy import GUROBI
        if GUROBI in INSTALLED_SOLVERS:
            import gurobipy
            objective = Minimize(self.x[0])
            constraints = [self.x[0] >= 1]
            prob = Problem(objective, constraints)
            try:
                prob.solve(solver=GUROBI, TimeLimit=0.0)
            except Exception as e:
                self.fail("An exception %s is raised instead of returning a result." % e)

            extra_stats = None
            solver_stats = getattr(prob, "solver_stats", None)
            if solver_stats:
                extra_stats = getattr(solver_stats, "extra_stats", None)
            self.assertTrue(extra_stats, "Solver stats have not been returned.")

            nb_solutions = getattr(extra_stats, "SolCount", None)
            if nb_solutions:
                self.skipTest("Gurobi has found a solution, the test is not relevant anymore.")

            solver_status = getattr(extra_stats, "Status", None)
            if solver_status != gurobipy.GRB.TIME_LIMIT:
                self.skipTest("Gurobi terminated for a different reason than reaching time limit, "
                              "the test is not relevant anymore.")

        else:
            with self.assertRaises(Exception) as cm:
                prob = Problem(Minimize(norm(self.x, 1)), [self.x == 0])
                prob.solve(solver=GUROBI, TimeLimit=0)
            self.assertEqual(str(cm.exception), "The solver %s is not installed." % GUROBI)

    def test_gurobi_environment(self) -> None:
        """Tests that Gurobi environments can be passed to Model.
        Gurobi environments can include licensing and model parameter data.
        """
        from cvxpy import GUROBI
        if GUROBI in INSTALLED_SOLVERS:
            import gurobipy

            # Set a few parameters to random values close to their defaults
            params = {
                'MIPGap': np.random.random(),  # range {0, INFINITY}
                'AggFill': np.random.randint(10),  # range {-1, MAXINT}
                'PerturbValue': np.random.random(),  # range: {0, INFINITY}
            }

            # Create a custom environment and set some parameters
            custom_env = gurobipy.Env()
            for k, v in params.items():
                custom_env.setParam(k, v)

            # Testing QP Solver Interface
            sth = StandardTestLPs.test_lp_0(solver='GUROBI', env=custom_env)
            model = sth.prob.solver_stats.extra_stats
            for k, v in params.items():
                # https://www.gurobi.com/documentation/9.1/refman/py_model_getparaminfo.html
                name, p_type, p_val, p_min, p_max, p_def = model.getParamInfo(k)
                self.assertEqual(v, p_val)

        else:
            with self.assertRaises(Exception) as cm:
                prob = Problem(Minimize(norm(self.x, 1)), [self.x == 0])
                prob.solve(solver=GUROBI, TimeLimit=0)
            self.assertEqual(str(cm.exception), "The solver %s is not installed." % GUROBI)


class TestConicQuadObj(QPTestBase):
    """Test conic solvers with use_quad_obj=True."""

    def setUp(self) -> None:
        super().setUp()

        # Conic solvers that support quadratic objectives
        # Exclude KNITRO - its conic interface with use_quad_obj is unstable in CI
        self.solvers = [
            solver for solver in INSTALLED_CONIC_SOLVERS
            if solver in SOLVER_MAP_CONIC
            and SOLVER_MAP_CONIC[solver].supports_quad_obj()
            and solver != cp.KNITRO
        ]
        self.solvers = self.filter_licensed_solvers(self.solvers)

    def solve_QP(self, problem, solver_name):
        """Solve with use_quad_obj=True and verify no SOC cones are introduced."""
        data, _, _ = problem.get_problem_data(
            solver_name,
            solver_opts={"use_quad_obj": True}
        )
        self.assertEqual(data["dims"].soc, [],
            f"Problem should have no SOC cones for QP canonicalization with {solver_name}")
        return problem.solve(solver=solver_name, use_quad_obj=True, verbose=False)

    def test_all_solvers(self) -> None:
        """Test conic solvers with use_quad_obj=True.

        Only runs tests that have constraints (filtering out unconstrained
        problems for solvers with REQUIRES_CONSTR=True).

        Tests with m=0 after canonicalization (skip for REQUIRES_CONSTR solvers):
        - power, quad_form, quad_form_coeff, rep_quad_form
        """
        for solver in self.solvers:
            requires_constr = SOLVER_MAP_CONIC[solver].REQUIRES_CONSTR

            self.quad_over_lin(solver)
            if not requires_constr:
                self.power(solver)
            self.power_matrix(solver)
            self.square_affine(solver)
            if not requires_constr:
                self.quad_form(solver)
            self.affine_problem(solver)
            self.maximize_problem(solver)
            self.abs(solver)
            if not requires_constr:
                self.quad_form_coeff(solver)
            self.quad_form_bound(solver)
            self.regression_1(solver)
            self.regression_2(solver)
            if not requires_constr:
                self.rep_quad_form(solver)
            self.control(solver)
            self.sparse_system(solver)
            self.smooth_ridge(solver)
            self.huber_small(solver, places=3)
            self.huber(solver)
            self.equivalent_forms_1(solver)
            self.equivalent_forms_2(solver)
            self.equivalent_forms_3(solver)


@unittest.skipUnless('MPAX' in INSTALLED_SOLVERS, 'MPAX is not installed.')
class TestMPAX(unittest.TestCase):

    def test_mpax_lp_0(self) -> None:
        StandardTestLPs.test_lp_0(solver='MPAX')

    def test_mpax_lp_1(self) -> None:
        StandardTestLPs.test_lp_1(solver='MPAX')

    def test_mpax_lp_2(self) -> None:
        StandardTestLPs.test_lp_2(solver='MPAX')

    def test_mpax_lp_3(self) -> None:
        sth = sths.lp_3()
        with self.assertWarns(Warning):
            sth.prob.solve(solver='MPAX')
            self.assertEqual(sth.prob.status, cp.settings.INFEASIBLE_OR_UNBOUNDED)

    def test_mpax_lp_4(self) -> None:
            sth = sths.lp_4()
            with self.assertWarns(Warning):
                sth.prob.solve(solver='MPAX')
                self.assertEqual(sth.prob.status, cp.settings.INFEASIBLE_OR_UNBOUNDED)

    def test_mpax_lp_5(self) -> None:
        StandardTestLPs.test_lp_5(solver='MPAX')

    def test_mpax_lp_6(self) -> None:
        StandardTestLPs.test_lp_6(solver='MPAX')

    def test_mpax_warmstart(self) -> None:
        x = cp.Variable(shape=(2,), name='x')
        objective = cp.Minimize(-4 * x[0] - 5 * x[1])
        constraints = [2 * x[0] + x[1] <= 3,
                    x[0] + 2 * x[1] <= 3,
                    x[0] >= 0,
                    x[1] >= 0]
        prob = cp.Problem(objective, constraints)
        result1 = prob.solve(solver='MPAX', warm_start=False)
        self.assertAlmostEqual(result1, -9, places=4)
        result2 = prob.solve(solver='MPAX', warm_start=True)
        self.assertAlmostEqual(result2, -9, places=4)

    def test_MPAX_qp_0(self) -> None:
        StandardTestQPs.test_qp_0(solver='MPAX')
